Brandon C Reyes1, Irene Otero-Muras2, Vladislav A Petyuk3. 1. Advanced Computing, Math, and Data Division, Pacific Northwest National Laboratory, Richland, WA, 99352, USA. 2. BioProcess Engineering Group, IIM-CSIC (Spanish National Research Council), 36208, Vigo, Spain. 3. Biological Sciences Division, Pacific Northwest National Laboratory, Richland, WA, 99352, USA. vladislav.petyuk@pnnl.gov.
Abstract
BACKGROUND: Theoretical analysis of signaling pathways can provide a substantial amount of insight into their function. One particular area of research considers signaling pathways capable of assuming two or more stable states given the same amount of signaling ligand. This phenomenon of bistability can give rise to switch-like behavior, a mechanism that governs cellular decision making. Investigation of whether or not a signaling pathway can confer bistability and switch-like behavior, without knowledge of specific kinetic rate constant values, is a mathematically challenging problem. Recently a technique based on optimization has been introduced, which is capable of finding example parameter values that confer switch-like behavior for a given pathway. Although this approach has made it possible to analyze moderately sized pathways, it is limited to reaction networks that presume a uniterminal structure. It is this limited structure we address by developing a general technique that applies to any mass action reaction network with conservation laws. RESULTS: In this paper we developed a generalized method for detecting switch-like bistable behavior in any mass action reaction network with conservation laws. The method involves (1) construction of a constrained optimization problem using the determinant of the Jacobian of the underlying rate equations, (2) minimization of the objective function to search for conditions resulting in a zero eigenvalue, (3) computation of a confidence level that describes if the global minimum has been found and (4) evaluation of optimization values, using either numerical continuation or directly simulating the ODE system, to verify that a bistability region exists. The generalized method has been tested on three motifs known to be capable of bistability. CONCLUSIONS: We have developed a variation of an optimization-based method for the discovery of bistability, which is not limited to uniterminal chemical reaction networks. Successful completion of the method provides an S-shaped bifurcation diagram, which indicates that the network acts as a bistable switch for the given optimization parameters.
BACKGROUND: Theoretical analysis of signaling pathways can provide a substantial amount of insight into their function. One particular area of research considers signaling pathways capable of assuming two or more stable states given the same amount of signaling ligand. This phenomenon of bistability can give rise to switch-like behavior, a mechanism that governs cellular decision making. Investigation of whether or not a signaling pathway can confer bistability and switch-like behavior, without knowledge of specific kinetic rate constant values, is a mathematically challenging problem. Recently a technique based on optimization has been introduced, which is capable of finding example parameter values that confer switch-like behavior for a given pathway. Although this approach has made it possible to analyze moderately sized pathways, it is limited to reaction networks that presume a uniterminal structure. It is this limited structure we address by developing a general technique that applies to any mass action reaction network with conservation laws. RESULTS: In this paper we developed a generalized method for detecting switch-like bistable behavior in any mass action reaction network with conservation laws. The method involves (1) construction of a constrained optimization problem using the determinant of the Jacobian of the underlying rate equations, (2) minimization of the objective function to search for conditions resulting in a zero eigenvalue, (3) computation of a confidence level that describes if the global minimum has been found and (4) evaluation of optimization values, using either numerical continuation or directly simulating the ODE system, to verify that a bistability region exists. The generalized method has been tested on three motifs known to be capable of bistability. CONCLUSIONS: We have developed a variation of an optimization-based method for the discovery of bistability, which is not limited to uniterminal chemical reaction networks. Successful completion of the method provides an S-shaped bifurcation diagram, which indicates that the network acts as a bistable switch for the given optimization parameters.
Authors: Nicolas Le Novère; Michael Hucka; Huaiyu Mi; Stuart Moodie; Falk Schreiber; Anatoly Sorokin; Emek Demir; Katja Wegner; Mirit I Aladjem; Sarala M Wimalaratne; Frank T Bergman; Ralph Gauges; Peter Ghazal; Hideya Kawaji; Lu Li; Yukiko Matsuoka; Alice Villéger; Sarah E Boyd; Laurence Calzone; Melanie Courtot; Ugur Dogrusoz; Tom C Freeman; Akira Funahashi; Samik Ghosh; Akiya Jouraku; Sohyoung Kim; Fedor Kolpakov; Augustin Luna; Sven Sahle; Esther Schmidt; Steven Watterson; Guanming Wu; Igor Goryanin; Douglas B Kell; Chris Sander; Herbert Sauro; Jacky L Snoep; Kurt Kohn; Hiroaki Kitano Journal: Nat Biotechnol Date: 2009-08-07 Impact factor: 54.908
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